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Some technologies of ultra-precision single-plane polishing and lapping devices, including spindle section, polishing pad, cooling system, dressing system and pressurization system are discussed. The development trends of ultra-precision single-plane polishing and lapping devices are also analyszed as more controllable, integrated and high-precision in the future.

The fractional differential equation has a memory property and is suitable for biomathematical modeling. In this paper, a fractional SEQIR epidemic model with saturated incidence and vaccination is constructed. Firstly, for the deterministic fractional system, the threshold conditions for the local and global asymptotic stability of the equilibrium point are obtained by using the stability theory of the fractional differential equation. If R0<1, the disease-free equilibrium is asymptotically stable, and the disease is extinct; when R0>1, the endemic equilibrium is asymptotically stable and the disease persists. Secondly, for the stochastic system of integer order, the stochastic stability near the positive equilibrium point is discussed. The results show that if the intensity of environmental noise is small enough, the system is stochastic stable, and the disease will persist. Thirdly, the control variables are coupled into the fractional differential equation to obtain the fractional control system, the objective function is constructed, and the optimal control solution is obtained by using the maximum principle. Finally, the correctness of the theoretical derivation is verified by numerical simulation.

There are four kinds of ultra-precision lapping machine bed were developed: with/without reinforcing rib, with/without a pair of closed sides. The finite element analysis was used to find the optimal design of the machine bed. The 3D model of the ultra-precision lapping machine bed was built by SolidWorks, and ANSYS software was used for static analysis and modal analysis. The results suggest that when reinforcing rib and a pair of closed sides were owned, the machine bed had some better static and dynamic characteristics. The mix-deformation of this machine bed was 1.911μm, and the first-order inherent frequency was 101.74Hz.

An ultra-precision lapping machine is developed, with precision turning technology to condition lapping plate in situ, pressurizating by cylinder pressure, and cooling frictional heat with inner cooling system, the lapping machine is used for ultra-precision lapping of brittle materials. The design concept and the structure of the key components of the utra-precision sngle-plane lpping mchine are discussed. After precision turning, the flatness of lapping plate is down to 0.002 mm/400 mm, and experimental results show that the flatness of circular grating glass has been greatly improved after ultra-precison lapping.